Fourier Series for odd integers only

Can someone please help me to get this function B to only apply to odd integers but for every other odd integers the formula is negative. So for integer 1,5,9... its positive and for 3,7,11.... its negative

% Fourier Series 
syms x k L
f1(x) = x;
f2(x) = L-x;
f1 = simplify(f1);
f2 = simplify(f2);
%Solving for Bn
b(k) = (2/L)*int(f1*sin(k*pi*x/L),[0,L/2]);

b(k) = 

b1(k) = (2/L)*int(f2*sin(k*pi*x/L),[L/2,L]);

b1(k) = 

B(k) = b1 + b

B(k) = 

B = simplify(B)

[Image Analyst]

I formatted your code as code so people can easily copy it into their MATLAB, and I ran the code. But I'm not sure what you're asking. What are the "integers" that you're talking about?

[Paul]

I see that one issue in the code has been fixed, but I still think the equations for b(k) and b1(k) are incorrect based on my assumption of what the goal of this code actually is.

Answer 1

[Walter Roberson]

symsum( (-1)^(k+1)*B(2*k-1), k, 1, inf)

[Walter Roberson]

% Fourier Series 
syms x k L
f1(x) = x;
f2(x) = L-x;
f1 = simplify(f1);
f2 = simplify(f2);
%Solving for Bn
b(k) = (2/L)*int(f1*sin(k*pi*x/L),[0,L/2]);
b(k) = simplify(b(k))

b(k) = 

b1(k) = (2/L)*int(f2*sin(k*pi*x/L),[L/2,L]);
b1(k) = simplify(b(k))

b1(k) = 

B(k) = b1 + b

B(k) = 

syms N integer
val(N) = symsum( (-1)^(k+1)*B(2*k-1), k, 1, N)

val(N) = 

val(25)

ans = 

vpa(ans)

ans = 

val(100)

ans = 

vpa(ans)

ans = 

val(200)

ans = 

vpa(ans)

ans = 

val(1234)

ans = 

vpa(ans)

ans = 

val(inf)

ans = 

NaN

[Walter Roberson]

% Fourier Series 
syms x k L
f1(x) = x;
f2(x) = L-x;
f1 = simplify(f1);
f2 = simplify(f2);
%Solving for Bn
b(k) = (2/L)*int(f1*sin(k*pi*x/L),[0,L/2]);

b1(k) = (2/L)*int(f2*sin(k*pi*x/L),[L/2,L]);

B(k) = b1 + b

B(k) = 

B = simplify(B)

B(k) = 

syms N integer
val(N) = symsum( (-1)^(k+1)*B(2*k-1), k, 1, N)

val(N) = 

val(100), vpa(ans)

ans = 

ans = 

val(200), vpa(ans)

ans = 

ans = 

val(201), vpa(ans)

ans = 

ans = 

Answer 2

[Paul]

Hi Tashanda,

I see a couple of issues with the code

Though not an error, it would be clearer if you specified the variable of integration. And it's always best to use sym(pi). With these changes, the equation for b(k) would look like

%b(k) = (2/L)*int(f1*sin(k*pi*x/L),[0,L/2]);
b(k)  = (2/L)*int(f1*sin(k*sym(pi)*x/L),x,[0,L/2]);
b(k)  = simplify(b(k))

But even with those changes, the equation for b(k) is incorrect. Go back to your source and carefully compare this code to what the equation should be.

Then, the same comments apply to b1(k).

b1(k) = (2/L)*int(f2*sin(k*pi*x/L),[L/2,L]);

Finally, this line is a typo. i don't think you want b(k) on the right hand side.

b1(k) = simplify(b(k))